This paper is concerned with the method,which approaches to analytical solution of the light field equation with the Gauss-Hermite mode in three-dimension free space.The number of modes needed for calculating has been eatimated.The method has the following advantages:(1)Simulation electron number is reduced by about two orders of magnitude in comparison with DM methed;(2)Electron equations and G-H modes can be computed parallely.

Higher-order accuracy schemes are established following PADE' approach.Based on the schemes,fast recursive algorithms for the simple equations.Can be obtained and satisfy the corresponding conservation law.The fast recursive algorithm in the reference ^[1] is a kind of specific form of the present recursive algorithms given here.